_multiplyComplex, real part

Average Error: 0.0 → 0.0

Time: 2.2s

Precision: 64

Math

\[x.re \cdot y.re - x.im \cdot y.im\]

↓

\[(x.re \cdot y.re + \left(-x.im \cdot y.im\right))_*\]

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1374927 = x_re;
        double r1374928 = y_re;
        double r1374929 = r1374927 * r1374928;
        double r1374930 = x_im;
        double r1374931 = y_im;
        double r1374932 = r1374930 * r1374931;
        double r1374933 = r1374929 - r1374932;
        return r1374933;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1374934 = x_re;
        double r1374935 = y_re;
        double r1374936 = x_im;
        double r1374937 = y_im;
        double r1374938 = r1374936 * r1374937;
        double r1374939 = -r1374938;
        double r1374940 = fma(r1374934, r1374935, r1374939);
        return r1374940;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

1. Initial program 0.0

   \[x.re \cdot y.re - x.im \cdot y.im\]
2. Using strategy rm

3. Applied fma-neg 0.0

   \[\leadsto \color{blue}{(x.re \cdot y.re + \left(-x.im \cdot y.im\right))_*}\]

4. Final simplification 0.0

   \[\leadsto (x.re \cdot y.re + \left(-x.im \cdot y.im\right))_*\]

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))